11 November 2017

Simplified Measurements

As units of weights and measures have evolved in the course of time, each subdivision had their own specific use, each trade their own measurement. Food stuff were measured in pounds because a pound of potatoes, for example, is just how much one eats in a few days. Precious metals and medications were measured in ounces, because an ounce of silver could be a week's wage worth for a worker. An acre is the land surface one can plow with a horse in roughly a day. Two hundred square foot is the size of a comfortable family kitchen (at times when it was the only heated room in the house and families did not much space).
As there was no much need to mix those different domains of life, there was also no pressure to force all measurements into a single system.
However, with the advent of science and technology there were more and more connections between all the different things. How many pills can be made from a pound of base material? How many family homes can be build on one acre?

This is just a very brief glimpse on the motivation behind introducing a decimal system where number conversions simply happen by shifting the comma. (Once the decimal system was used in a majority of places, many others followed not for its intrinsic practicality, but just to ease international trade.)

But what about time?

So now most of the world measures weights as 1 ton = 1'000 kg = 1'000'000 grams and lengths in meters with set of prefixes which in daily life go from 1 km = 1'000 m = 100'000 cm = 1'000'000 mm and in specialist industries can go much further up and down. Of the three physical base units, weight and space and time, however, time has escaped decimalization. It even has escaped twice, once with the small units of time which come in packs of 60 and 24, and even more radically on the calendrical level where the subdivisions are not only chaotic like having on one hand 52 weeks of 7 days, on the other hand 12 months of 28 to 31 days and years of either 365 or 366 days that need to be broken up! Now, we're looking at very different kinds of problems when trying to sort this out: on the one hand, days and years are given to us by the universe and each correspond to a different amount of time that does not provide an integer subdivision. When we think of "ending the year" on midnight December 31st, this is a calendrical illusion because the Earth will not be exactly at the same point around the sun as it was at the same time exactly 365 or 366 days before. This is a problem that we have to solve with good conventions and we can do so with some liberty because no human will notice the seasons shifting for a small number of days as long as those small numbers don't add up over the years.

The other problem, however, is caused by the completely human set intervals of weeks and months which only increase the irregularity instead of decreasing it. Without even thinking of introducing decimal 10-day weeks like the French Revolution did (and the Soviet Revolution tried it again), let's look at the issues that are actually solvable:

Saying how many weekdays (working days) and how many weekend days are in any given year with not more than one extra bit of information. Today you need to know which year it is or at least with which day of week it starts and whether it is a leap year. In a simple calendar the answer should only depend on the leap year bit and optimally also not differ too much.

Saying how many workdays and non-workdays are in each month and each quarter.

Then, answer the above questions also taking public holidays into account which may or may not fall on a weekend, reducing the number of workdays only if they don't.

Saying how many days or weeks there are between two different dates in the same year or of a different year.

Saying what day of the week a specific day will we.

Currently, answer to the counting questions are: 5*52 plus zero, one, or two, that is, 260, 261, or 262 workdays per year, and 104, 105, or 106 weekend days per year. With public holidays it depends on the country and region (and sometimes, the city).

For a quarter, there are currently 90, 91, or 92 days where two difference days can again be either weekends or workdays, so the relative uncertainty is even bigger.

A Simplified Calendar does not need change radically

Now, the surprise I want to explain here is that we can already simplify those questions and more by making two small changes to the current calendar! There is no need to change all months to be exactly 4 weeks long (thus getting 13 months per year and killing the concept of a quarter-year) and also no need to change any of the month's lengths at all except for the placement of the leap day (which is currently February 29th) and breaking of a two-thousand year old dogma.

Let's start with the easier of the two and make good use of the fact that the 52 weeks in a year very neatly fall in 4 packs of 13. So a quarter-year as used by most business for accounting purposes could always have 13 full weeks and therefore a fixed number of 65 working days and 26 weekend days. In the Gregorian Calendar as we use it today, starting a quarter at the first day of January, April, July, and October, the length of the quarters is 92 in Q3 and Q4, 91 in Q2, and 90 or 91 in Q1 depending on it being a leap year or common year. So if we moved the leap day to Q3 or Q4 then each quarter would have 91 or 92 days, which means there will always be at least 13 full weeks plus optionally an extra day. If we could arrange for that extra day to always fall on a weekend, we would even get four quarters with exactly 65 working days and 26 or 27 non-working days! And all of that with a change that still keeps all the 366 dates of the Gregorian Calendar. (Only that February 29th will be there every year and some other day in Q3 or Q4 will only exists in leap years.)

Now, did you get suspicious when you read the phrase "arrange for that extra day to always fall on a weekend" above? Any given date (that is month plus day-in-month) can of course fall on any day of the week. For example, Gregorian leap year 2012 had the very nice property of starting the first, second, and third quarter on a Sunday. And the common year 2017 had the nice property that the first and last quarter started with a Sunday while the year also ended with a Sunday. If we just took the calendars for those years and put them together we'd get a year in which each quarter starts with a Sunday and ends (if it has 91 days) on a Saturday, or if it has 92 days on a Sunday. This would automatically mean that the quarters all have exactly 65 working days! Ain't that great?!

Do you see the problem yet? All quarters starting on a Sunday and ending on a Saturday means that the last day of each quarter, a Saturday, will be followed by the first day of the next quarter, a Sunday, which is what happend to all Saturdays in the 2000 year history of the Gregorian and Julian calendars! However, for those quarters which end in a Sunday, the next day –oh dogma!– would again be a Sunday so that each quarter can indeed start its rhythm in the same, fixed scheme. Note that I just chose Sunday for the sake of example, because it seemed practical to have an extra week-end day. If it seems less blasphemous to my reader, we can repeat the same argument with the common year 2016 and a suitably chosen leap year both starting on a Saturday and then get one or two extra Saturdays per year. We could also just call them Leap Day or Extra-Weekend-Day. Or give them any other name as if we were creating a public holiday.

As a side note: an average Gregorian year has 365.2425 * 5/7 = 260.8875 work days whereas the regular calendar described here always has only 260 working days. So that's almost one extra public holiday. (Since all other public holidays will now fall on fixed days of the week, governments will probably want to recount the net sum of public holidays on work days and shift some of those around, so that this additional day could also be dedicated to some higher meaning.)

If you can hold the idea of having one extra long weekend every year (and two in leap years) then we can think a little about where in the year those extra long weekends should be! In fact, by suggesting that we simply repeat one of the good Gregorian years every year, I already arrived at the conclusion that the first and last day of the year would be the same day of the week, so there's an obvious place to put that extra long week-end: as in most countries 1st January is already a public holiday and 31st December is a big party. Of course that party would be easier to organize if it were on a weekend and that's exactly what we'll achieve! During a time where many people take vacation anyways, this does not interrupt the flow of society and rather helps people save up their vacation days for other times of the year.

From what I wrote above, it is also clear that the other long week-end should be placed in the third quarter (July, August, or September). Since it is a leap day which will not be there in all of the years, it should be the last day of any of those months. Since with the proposed scheme of starting and ending the year and all quarters on week-ends, only the end of September is on a week-end, September 30th suggests itself as the leap day.

To sum up how this regularized calendar looks like:

All months keep their existing length, but February 29th is in every year and September, 30th is only in leap years.

The first days of each quarter, that is 1st of January, April, July, and October, as well as the last days of September and December will be a Sunday (or if you like that variant: a Saturday).

Each business quarter will have exactly 65 working days and 13 weekends with usually two days. All quarters start at the same day of the week.

The weekend which spans the new year has three days. (Either because December 31st and January 1st are the same day of the week or because December 31st is a special day of the week.)

In leap years, the weekend around September 30st also has three days.

Every date has the same day of week and week-number in every year. So if someone needs to make day-of-week calculations even easier, they can always switch between a week-based date (Q1, week 6, Monday) and a month-based date, because the conversion is the same in every year.

Years are the same as Gregorian into the past and into the future. Dates between the new leap day (Sept 30th) and the old leap day (Feb 29th) are also the same in all years. Other dates only differ by one day and only in common years.

If you like all of this, you might also be interested to know:

how would this calendar actually look like on paper or in your calendar app?

what would change about the plan if Feb 29th stayed as leap day (so that all dates would still be equivalent with Gregorian days in all years)? Could we arrange for Feb 29th to fall on a weekend and place the other extra day such that it does not disrupt the usual flow of work and non-work days? Could we then still achieve a fixed number of working days per quarter? (Having a four-day week or an only one-day weekend in all common years just doesn't sound as attractive as an occasional three-day weekend.)

what would be some really cool names to give to those non-septemiary extra days of the week?

what would be a practical arrangement of holidays in your country in the proposed regular calendar which keeps a regular distribution of working days in each quarter? (Maybe follow the Canadian example of spreading the public holidays such that there is more or less one in every month.)

31 October 2017

From building my new bike, I am left over with a 20-hole hub and from another old project, a 28 hole rim. (For readers who are already confused: those counts are normal in the 20 inch and folding bike world, where the typical 36 spokes are not needed to make a strong and lasting wheel.)While thinking how those could be combined, I came up with a new spoke pattern which I had never seen before:

Solid lines are spokes from the facing side of the hub, dashed is the other side. This pattern uses five spokes of three different lengths and is repeated four times around the hub for full twenty spokes. It has lots of nice properties:

Unused holes on the rim (empty circles in the picture) are equally spaced with two and three spokes alternating in between.

Every second spoke arriving on the rim will be from one side of the hub, every other from the other side.

Spokes only need to be of three different lengths as opposed to seven different lengths when interleaving the non-used rim-holes with a regular 4-spoke pattern.

To achieve this, every second instance of the pattern is laced with 3 spokes on one side and every other with two spokes on that side (pattern reversed). The left sketch shows how this leads to the proper alteration of left (dashed) and right (solid) spokes on the rim.

Note that the right picture shows only the facing ten holes of the hub, and only a quarter (one pattern instance) of the spoke and rim.

I think that this would look quite intriguing in an actual wheel, especially if some of the spokes were of a different color. Either do the four radial spokes in white, rest in black; or do the eight single-crossed spokes in white, rest in black. In both cases, half the white spoke would emerge from each side of the hub and would form a cross when looking the wheel from the side. And the best thing I realized later: although designed for a 20/28 hub/rim recycling, this would work as well on straight 20/20 and even yield a quite durable front wheel(*)!(*) As long as no disc-brakes are involved.

29 August 2015

I have noticed this thing a few years ago and it seemed like a very obvious concept to me. As usually when I invent something, I googled it, but unlike most times when I can read about others who already invented the same thing, I did not find any similar concept this time.
So here is the idea: in some companies (or organisations in general) writing is used more than in others to pass information around and to discuss things. This is obviously a gradual concept: some things will always be in written form, some always in oral form, but for many things in between, there is a choice of sending an email, creating a wiki entry, drafting a design doc, or talking to your coworker, or talking to the entire team of people sitting in front of their computers, or calling a meeting to discuss things and take decisions.
Let me just give one example out of many: a software team can come together in meeting to discuss requirements, specs (or acceptance criteria) for a new feature with one of them taking notes during the meeting and thereby complete the spec (or "user story"). Another possible way would be for one person to write a draft spec (no matter if that's a business analyst, product manager, lead developer, or just the person with the most interest and knowledge in that particular feature) and email it to others. (It's another question of culture not treated here, whether others can directly put their feedback into a shared document (wiki, issue tracker, whatever) or have to send it back to the responsible person.) In any case, the former way would be much more oral (keeping in mind that at a minimum meeting invitations are usually sent by email) while the latter is much more written (maybe with an oral part, when the document author reminds one or two coworkers to give their feedback while he crossing them in the company kitchen or hallway).
I can easily come up with a pro/con list of oral and written communication. Advantages for oral communication are:

an asker of a question can get an immediate answer (which is very important when the question blocks their current task)

people get a break from staring at their monitors

being able to see another's facial expression transmits information that is often hard to put in words

talking to just one person or a group of people all listening at once is faster than writing something. (this is even more true for people who aren't quick in formulating written speech; on the other hand, it's not true at all when the speaker makes notes for what they are going to say before saying it)

Advantages for written communication are:

reading something is much quicker than listening to the same information spoken aloud. this is even more true when not all of it is relevant, because each reader can skip parts as they like, independent on all others.

written information stays available for reading it again later. especially with modern computer's search capacity this can be very valuable.

it's asynchronous: readers do not need to occupy the same time spot as the writer. each reader can read at their own preferred time.

both points 2 and 3 make written communication scale up much better: it is both hard to find a meeting time for more than six people and keeping all of them engaged all the time.

writing something down helps clarify one's thoughts in a similar way that talking to someone does. but in writing the writer does not use another person's time and he or she can include their clarified thoughts into the communication that's sent out, possibly avoiding one loop of discussion.

Writing allows to convey more complex information in more detail than oral speech can. In particular, for rational decision taking, writing has been shown to be extremely helpful, aiding in fighting many human heuristic biases that stand in the way of rationality.

Notice that text chat (such as via Skype, Jabber, SnapChat, etc.) is a form that combines advantages of both oral (it's instant) and written (it's silent and still somewhat asynchronous and can be looked up later) communication. Since it sits so neatly in between the two pure forms of oral and written, it can be used to differentiate company cultures on a single scale: a company has more written culture than an otherwise similar one if they use text chat in some places where the other uses talking. And the same goes for using email, a ticket system, or a wiki instead of text chat. (I would even argue that using a well structured wiki or task/project management system is more of a written culture than just using email all the time.

While I see that both sides (and all the shades in between) have their respective advantages, I find that most teams in the company I am currently working for, hang way to much towards the oral side than I would like. In particular, I am often disturbed by conversations in the team area that go over my head and distract from my current task. I find it hard to decide whether I should take of my sound-blockers to listen or (often unsuccessfully) try to ignore it. I hate spending time in meetings discussing things which one person could prepare beforehand, not just saving everybody time, but also often creating a result of higher quality. I hate it when a group has agreed on something, but later acts differently because the details and reasons had not been written down. I hate it when I miss an important discussion or information just because I was absent for a moment. And although I am not completely sure of it, I think that a written culture can encourage people to take more responsibility, for example, by drafting up suggestions to be approved instead of asking others and by just sitting down with a problem and a piece of paper (or text editor) before getting other's advice.

In other words: while I value the ease, quickness, and naturalness of simply talking to people, I would like my work environment to keep much more to the written way. After all, writing is part of what made our higher culture and our computing technology possible in the first place. Companies who neglect the writing, might not be able to tackle really complex issues and stay at the cutting edge of industry.